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Numerical Computation, Data Analysis and Software in Mathematics and Engineering
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Numerical Computation, Data Analysis and Software in Mathematics and Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (9 October 2021) | Viewed by 32073

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Yumin Cheng

E-Mail Website
Guest Editor
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China
Interests: numerical analysis; applied mathematics; computational mathematics; computational mechanics; civil and structural engineering; CAE software
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Dr. Yumin Cheng is Professor of the Shanghai Institute of Applied Mathematics and Mechanics of Shanghai University. He received his bachelor’s degree of mathematics from Shanxi University of China, and PhD degree of computational mechanics from Xi’an Jiaotong University of China. His research interests include the meshless method, boundary element method, and scientific and engineering computing. He has published more than 180 journal papers with 4600 citations. His h-index in scopus.com is 44. He has been honored with Fellow of The International Association of Applied Mechanics (IAAM), Fellow of International Association of Advanced materials and VEBLEO Fellow awards. He is an Executive Committee member of IAAM and Chairman of Committee of IAAM Standards and Codes. He has been Lead Guest Editor of the Special Issue of Mathematical Problems in Engineering (SI: Mathematical Aspects of Meshless Methods; SI: New Trends in Numerical Simulation and Data Analysis), and he is Associate Editor of the International Journal of Computers, Editor and Member of the Editorial Board of the International Journal of Applied Mechanics, and Member of the Editorial Board of the International Journal of Computational Materials Science and Engineering, Journal of Computational Engineering, International Journal of Applied & Experimental Mathematics, and International Journal of Mathematical Physics and Video Proceedings of Advanced Materials.

Based on numerical methods such as the finite element method, boundary element method, and meshless method, numerical simulations for various problems in science, engineering, and society fields have developed rapidly in the recent decades. Various numerical methods are presented for solving problems in different fields, and the corresponding computational efficiency, accuracy, and convergence are studied as well. With the development of big data, numerical simulation combined data analysis will play a more important role in studying problems in the science, engineering, and society fields.

In this Special Issue, we particularly take an interest in manuscripts that report the relevance of numerical computation and data analysis for mathematical and engineering problems. The Special Issue will become an international forum for researchers to summarize the most recent developments of numerical simulations and data analysis within the last five years, especially for new problems. Moreover, manuscripts on the mathematical theories of numerical computation and data analysis for complicated science, engineering or social problems are welcome. We also concern the development of the corresponding aspects based on big data, including the corresponding theory, numerical method, and applications.

Software is an important part of numerical computation and data analysis in mathematics and engineering. This Special Issue also concerns the developments of the software of numerical methods, including the finite element method, boundary element method, and meshless method, and the ones for data analysis.

Prof. Dr. Yumin Cheng
Guest Editor

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Keywords

  • Numerical method
  • Numerical simulation
  • Finite element method
  • Boundary element method
  • Meshless method
  • Mathematical model
  • Data analysis
  • Software

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Published Papers (15 papers)

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Editorial

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5 pages, 179 KiB  
Editorial
Preface to the Special Issue on “Numerical Computation, Data Analysis and Software in Mathematics and Engineering”
by Yumin Cheng
Mathematics 2022, 10(13), 2267; https://doi.org/10.3390/math10132267 - 29 Jun 2022
Cited by 1 | Viewed by 1124
Abstract
In recent years, mathematical models, numerical methods and data analysis have been paid more attention [...] Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)

Research

Jump to: Editorial

20 pages, 4146 KiB  
Article
The Improved Element-Free Galerkin Method for 3D Helmholtz Equations
by Heng Cheng and Miaojuan Peng
Mathematics 2022, 10(1), 14; https://doi.org/10.3390/math10010014 - 21 Dec 2021
Cited by 11 | Viewed by 2603
Abstract
The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the [...] Read more.
The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the final discretized equations of the IEFG method for 3D Helmholtz equations can be derived by using the corresponding Galerkin weak form. The influences of the node distribution, the weight functions, the scale parameters of the influence domain, and the penalty factors on the computational accuracy of the solutions are analyzed, and the numerical results of three examples show that the proposed method in this paper can not only enhance the computational speed of the element-free Galerkin (EFG) method but also eliminate the phenomenon of the singular matrix. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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13 pages, 4820 KiB  
Article
Impact of Strong Wind and Optimal Estimation of Flux Difference Integral in a Lattice Hydrodynamic Model
by Huimin Liu and Yuhong Wang
Mathematics 2021, 9(22), 2897; https://doi.org/10.3390/math9222897 - 14 Nov 2021
Cited by 2 | Viewed by 1350
Abstract
A modified lattice hydrodynamic model is proposed, in which the impact of strong wind and the optimal estimation of flux difference integral are simultaneously analyzed. Based on the control theory, the stability condition is acquired through linear analysis. The modified Korteweg-de Vries (mKdV) [...] Read more.
A modified lattice hydrodynamic model is proposed, in which the impact of strong wind and the optimal estimation of flux difference integral are simultaneously analyzed. Based on the control theory, the stability condition is acquired through linear analysis. The modified Korteweg-de Vries (mKdV) equation is derived via nonlinear analysis, in order to express a description of the evolution of density waves. Then, numerical simulation is conducted. From the simulation results, strong wind can largely influence the traffic flow stability. The stronger the wind becomes, the more stable the traffic flow is, to some extent. Similarly, the optimal estimation of flux difference integral also contributes to stabilizing traffic flow. The simulation results show no difference compared with the theoretical findings. In conclusion, the new model is able to make the traffic flow more stable. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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23 pages, 5277 KiB  
Article
Research on Dynamic Response Characteristics for Basement Structure of Heavy Haul Railway Tunnel with Defects
by Jinfei Chai
Mathematics 2021, 9(22), 2893; https://doi.org/10.3390/math9222893 - 13 Nov 2021
Cited by 6 | Viewed by 1621
Abstract
Based on the basic principle of thermodynamics, an elastoplastic damage constitutive model of concrete is constructed in this paper. The model is realized and verified in FLAC3D, which provides a solid foundation for the study of dynamic response and fatigue damage to the [...] Read more.
Based on the basic principle of thermodynamics, an elastoplastic damage constitutive model of concrete is constructed in this paper. The model is realized and verified in FLAC3D, which provides a solid foundation for the study of dynamic response and fatigue damage to the base structure of a heavy haul railway tunnel. The dynamic response and damage distribution of the base structure of a heavy-duty railway tunnel with defects were numerically simulated by the concrete elastic-plastic damage constitutive model. Then, by analyzing the response characteristics of the tunnel basement structure under different surrounding rock softening degrees, different foundation suspension range and different foundation structure damage degree are determined. The results show the following: (1) The elastoplastic damage constitutive model of concrete can well describe the stress–strain relationship of materials, especially with the simulation results of post peak softening being in good agreement with the test results, and the simulation effect of the unloading–reloading process of the cyclic loading and unloading test also meet the requirements. (2) The initial stress field and dynamic response of the tunnel basement structure under the action of train vibration load are very different from the ideal state of the structure design when the surrounding rock of the base is softened, the base is suspended, or the basement structure is damaged. With the surrounding rock softening, basement hanging, or basement structure damage developing to a certain extent, the basement structure will be damaged. (3) The horizontal dynamic stress amplitude increases with the increase in the softening degree of the basement surrounding rock. The horizontal dynamic stress of the measuring point increases with the increase in the width of the hanging out area when the hanging out area is located directly below the loading line. When the degree of damage to the basement structure is aggravated, the horizontal dynamic tensile stress of each measuring point gradually decreases. (4) The maximum principal stress increment increases with the increase in the fracture degree of the basement structure, while the minimum principal stress increment decreases with the increase in the fracture degree of the basement structure, but the variation range of the large and minimum principal stress increments is small. The research results have important theoretical and practical significance for further analysis of the damage mechanism and control technology of the foundation structure of a heavy haul railway tunnel with defects. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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17 pages, 4356 KiB  
Article
An Extended Car-Following Model Based on Visual Angle and Electronic Throttle Effect
by Hongxia Ge, Siteng Li and Chunyue Yan
Mathematics 2021, 9(22), 2879; https://doi.org/10.3390/math9222879 - 12 Nov 2021
Cited by 4 | Viewed by 1496
Abstract
With the continuous advancement of electronic technology, auto parts manufacturing institutions are gradually applying electronic throttles to automobiles for precise control. Based on the visual angle model (VAM), a car-following model considering the electronic throttle angle of the preceding vehicle is proposed. The [...] Read more.
With the continuous advancement of electronic technology, auto parts manufacturing institutions are gradually applying electronic throttles to automobiles for precise control. Based on the visual angle model (VAM), a car-following model considering the electronic throttle angle of the preceding vehicle is proposed. The stability conditions are obtained through linear stability analysis. By means of nonlinear analysis, the time-dependent Ginzburg–Landau (TDGL) equation is derived first, and then the modified Korteweg-de-Vries (mKdV) equation is derived. The relationship between the two is thus obtained. Finally, in the process of numerical simulations and exploration, it is shown how the visual angle and electronic throttle affect the stability of traffic flow. The simulation results in MATLAB software verify the validity of the model, indicating that the visual angle and electronic throttle can improve traffic stability. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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19 pages, 7817 KiB  
Article
Numerical Modeling on Crack Propagation Based on a Multi-Grid Bond-Based Dual-Horizon Peridynamics
by Zili Dai, Jinwei Xie, Zhitang Lu, Shiwei Qin and Lin Wang
Mathematics 2021, 9(22), 2848; https://doi.org/10.3390/math9222848 - 10 Nov 2021
Cited by 5 | Viewed by 2420
Abstract
Peridynamics (PD) is a novel nonlocal theory of continuum mechanics capable of describing crack formation and propagation without defining any fracture rules in advance. In this study, a multi-grid bond-based dual-horizon peridynamics (DH-PD) model is presented, which includes varying horizon sizes and can [...] Read more.
Peridynamics (PD) is a novel nonlocal theory of continuum mechanics capable of describing crack formation and propagation without defining any fracture rules in advance. In this study, a multi-grid bond-based dual-horizon peridynamics (DH-PD) model is presented, which includes varying horizon sizes and can avoid spurious wave reflections. This model incorporates the volume correction, surface correction, and a technique of nonuniformity discretization to improve calculation accuracy and efficiency. Two benchmark problems are simulated to verify the reliability of the proposed model with the effect of the volume correction and surface correction on the computational accuracy confirmed. Two numerical examples, the fracture of an L-shaped concrete specimen and the mixed damage of a double-edged notched specimen, are simulated and analyzed. The simulation results are compared against experimental data, the numerical solution of a traditional PD model, and the output from a finite element model. The comparisons verify the calculation accuracy of the corrected DH-PD model and its advantages over some other models like the traditional PD model. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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20 pages, 4723 KiB  
Article
A Smart Helmet-Based PLS-BPNN Error Compensation Model for Infrared Body Temperature Measurement of Construction Workers during COVID-19
by Li Li, Jiahui Yu, Hang Cheng and Miaojuan Peng
Mathematics 2021, 9(21), 2808; https://doi.org/10.3390/math9212808 - 5 Nov 2021
Cited by 9 | Viewed by 2860
Abstract
In the context of the long-term coexistence between COVID-19 and human society, the implementation of personnel health monitoring in construction sites has become one of the urgent needs of current construction management. The installation of infrared temperature sensors on the helmets required to [...] Read more.
In the context of the long-term coexistence between COVID-19 and human society, the implementation of personnel health monitoring in construction sites has become one of the urgent needs of current construction management. The installation of infrared temperature sensors on the helmets required to be worn by construction personnel to track and monitor their body temperature has become a relatively inexpensive and reliable means of epidemic prevention and control, but the accuracy of measuring body temperature has always been a problem. This study developed a smart helmet equipped with an infrared temperature sensor and conducted a simulated construction experiment to collect data of temperature and its influencing factors in indoor and outdoor construction operation environments. Then, a Partial Least Square–Back Propagation Neural Network (PLS-BPNN) temperature error compensation model was established to correct the temperature measurement results of the smart helmet. The temperature compensation effects of different models were also compared, including PLS-BPNN with Least Square Regression (LSR), Partial Least Square Regression (PLSR), and single Back Propagation Neural Network (BPNN) models. The results showed that the PLS-BPNN model had higher accuracy and reliability, and the determination coefficient of the model was 0.99377. After using PLS-BPNN model for compensation, the relative average error of infrared body temperature was reduced by 2.745 °C and RMSE was reduced by 0.9849. The relative error range of infrared body temperature detection was only 0.005~0.143 °C. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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21 pages, 2811 KiB  
Article
Deep Learning Approach to Mechanical Property Prediction of Single-Network Hydrogel
by Jing-Ang Zhu, Yetong Jia, Jincheng Lei and Zishun Liu
Mathematics 2021, 9(21), 2804; https://doi.org/10.3390/math9212804 - 4 Nov 2021
Cited by 16 | Viewed by 3425
Abstract
Hydrogel has a complex network structure with inhomogeneous and random distribution of polymer chains. Much effort has been paid to fully understand the relationship between mesoscopic network structure and macroscopic mechanical properties of hydrogels. In this paper, we develop a deep learning approach [...] Read more.
Hydrogel has a complex network structure with inhomogeneous and random distribution of polymer chains. Much effort has been paid to fully understand the relationship between mesoscopic network structure and macroscopic mechanical properties of hydrogels. In this paper, we develop a deep learning approach to predict the mechanical properties of hydrogels from polymer network structures. First, network structural models of hydrogels are constructed from mesoscopic scale using self-avoiding walk method. The constructed model is similar to the real hydrogel network. Then, two deep learning models are proposed to capture the nonlinear mapping from mesoscopic hydrogel network structural model to its macroscale mechanical property. A deep neural network and a 3D convolutional neural network containing the physical information of the network structural model are implemented to predict the nominal stress–stretch curves of hydrogels under uniaxial tension. Our results show that the end-to-end deep learning framework can effectively predict the nominal stress–stretch curves of hydrogel within a wide range of mesoscopic network structures, which demonstrates that the deep learning models are able to capture the internal relationship between complex network structures and mechanical properties. We hope this approach can provide guidance to structural design and material property design of different soft materials. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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15 pages, 6963 KiB  
Article
A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems
by Fengxin Sun, Jufeng Wang, Xiang Kong and Rongjun Cheng
Mathematics 2021, 9(19), 2524; https://doi.org/10.3390/math9192524 - 8 Oct 2021
Cited by 6 | Viewed by 1591
Abstract
By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the [...] Read more.
By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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22 pages, 45134 KiB  
Article
Structural Optimization and Application Research of Alkali-Activated Slag Ceramsite Compound Insulation Block Based on Finite Element Method
by Xiaona Fan, Yu Guo, Qin Zhao and Yiyun Zhu
Mathematics 2021, 9(19), 2488; https://doi.org/10.3390/math9192488 - 4 Oct 2021
Cited by 2 | Viewed by 1593
Abstract
The research and application of new wall materials have been attracting increasing attention owing to the continuous promotion of sustainable development in the building industry. An alkali-activated slag ceramsite compound insulation block (AASCCIB) is used as the research object. Based on the finite [...] Read more.
The research and application of new wall materials have been attracting increasing attention owing to the continuous promotion of sustainable development in the building industry. An alkali-activated slag ceramsite compound insulation block (AASCCIB) is used as the research object. Based on the finite element method, the effects of different numbers of hole rows and hole ratios on the thermal and mechanical performances of AASCCIBs are analyzed using ANSYS CFX. On this basis, the AASCCIB with the optimal comprehensive performance is determined by a multi-objective optimization analysis. Finally, the improvement effect of the AASCCIB wall on the indoor thermal environment relative to an ordinary block (OB) wall is quantitatively analyzed using ANSYS CFX. The results show that the von Mises equivalent stress and heat transfer coefficient of the AASCCIB decrease with the increase in the hole ratio when the hole shape and number of hole rows are constant. AASCCIB B1 has the optimal comprehensive performance among six AASCCIBs, with the heat transfer coefficient and average von Mises equivalent stress of 0.446 W/(m2∙K) and 9.52 MPa, respectively. Compared with the indoor lowest and average temperatures of the building with the OB wall, those of the building with the AASCCIB wall increased by at least 1.39 and 0.82 °C on the winter solstice, respectively. The indoor temperature difference decreased by at least 0.83 °C. In addition, the indoor highest temperature, average temperature, and temperature difference decreased by at least 1.75, 0.79, and 1.89 °C on the summer solstice, respectively. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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13 pages, 5127 KiB  
Article
Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect
by Huimin Liu, Rongjun Cheng and Tingliu Xu
Mathematics 2021, 9(19), 2464; https://doi.org/10.3390/math9192464 - 3 Oct 2021
Cited by 2 | Viewed by 1381
Abstract
In actual driving, the driver can estimate the traffic condition ahead at the next moment in terms of the current traffic information, which describes the driver’s predictive effect. Due to this factor, a novel two-dimensional lattice hydrodynamic model considering a driver’s predictive effect [...] Read more.
In actual driving, the driver can estimate the traffic condition ahead at the next moment in terms of the current traffic information, which describes the driver’s predictive effect. Due to this factor, a novel two-dimensional lattice hydrodynamic model considering a driver’s predictive effect is proposed in this paper. The stability condition of the novel model is obtained by performing the linear stability analysis method, and the phase diagram between the driver’s sensitivity coefficient and traffic density is drawn. The nonlinear analysis of the model is conducted and the kink-antikink of modified Korteweg-de Vries (mKdV) equation is derived, which describes the propagation characteristics of the traffic density flow waves near the critical point. The numerical simulation is executed to explore how the driver’s predictive effect affects the traffic flow stability. Numerical results coincide well with theoretical analysis results, which indicates that the predictive effect of drivers can effectively avoid traffic congestion and the fraction of eastbound cars can also improve the stability of traffic flow to a certain extent. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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22 pages, 5260 KiB  
Article
A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions
by Jufeng Wang, Fengxin Sun and Rongjun Cheng
Mathematics 2021, 9(19), 2424; https://doi.org/10.3390/math9192424 - 29 Sep 2021
Cited by 6 | Viewed by 1898
Abstract
By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, [...] Read more.
By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS-IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS-IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS-IMLS method. In the improved IEFG method, the DS-IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS-IMLS and the improved IEFG methods have high accuracy. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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14 pages, 2501 KiB  
Article
Mathematical Models and Data Analysis of Residential Land Leasing Behavior of District Governments of Beijing in China
by Jing Cheng
Mathematics 2021, 9(18), 2314; https://doi.org/10.3390/math9182314 - 18 Sep 2021
Cited by 26 | Viewed by 2126
Abstract
To analyze the leasing behavior of residential land in Beijing, the mathematical models of the price and the total area of the leased residential land are presented. The variables of the mathematical models are proposed by analyzing the factors influencing the district government’s [...] Read more.
To analyze the leasing behavior of residential land in Beijing, the mathematical models of the price and the total area of the leased residential land are presented. The variables of the mathematical models are proposed by analyzing the factors influencing the district government’s leasing behavior for residential land based on the leasing right for residential land in Beijing, China. The regression formulae of the mathematical models are obtained with the ordinary least squares method. By introducing the data of the districts in Beijing from 2004 to 2015 into the mathematical models, the numerical results of the coefficients in the mathematical models are obtained by solving the equations of the regression formulae. After discussing the numerical results of the influencing factors, the district government behavior for leasing residential land in Beijing, China, is investigated. The numerical results show the factors concerning the government and how these factors influence the leased price and the total leased area of residential land for this large city in China. Finally, policy implications for the district government regarding residential land leasing in Beijing are proposed. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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18 pages, 4117 KiB  
Article
Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method
by Yajie Deng, Xingkeng Shen, Jixiao Tao and Ying Dai
Mathematics 2021, 9(16), 1967; https://doi.org/10.3390/math9161967 - 17 Aug 2021
Cited by 3 | Viewed by 1751
Abstract
A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The [...] Read more.
A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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11 pages, 34659 KiB  
Article
A Method for Rapid Prediction of Edge Defects in Cold Roll Forming Process
by Zhijuan Meng, Yanan Fang and Lidong Ma
Mathematics 2021, 9(16), 1902; https://doi.org/10.3390/math9161902 - 10 Aug 2021
Cited by 2 | Viewed by 2321
Abstract
In order to implement rapid prediction of edge defects in the cold roll forming process, a new analytical method based on the mean longitudinal strain of the racks is presented. A cubic spline curve with the parameters of the cumulative chord length is [...] Read more.
In order to implement rapid prediction of edge defects in the cold roll forming process, a new analytical method based on the mean longitudinal strain of the racks is presented. A cubic spline curve with the parameters of the cumulative chord length is applied to fit the corresponding points and center points of different passes, and fitting curves are obtained. As the cold roll forming is micro-tension forming, the tensions between racks are ignored. Then the mean longitudinal strains between racks are obtained. By comparing the mean longitudinal strain between racks and the yield strain of the material, we can judge whether there are defects at the edges. Finally, the reasonableness of this method is illustrated and validated by an example. With this method, the roll forming effect can be quickly predicted, and the position where a greater longitudinal strain occurred can be determined. In order to prevent the defects, the deformation angles need to be modified when the result is beyond the yield strain. To further prove the correctness of the theory, the results of the analytical method are compared with the ones of the non-linear finite element software ABAQUS. The analytical results have the same trend as the finite element results. This method can provide useful guidance to the actual design process. Full article
(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)
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